A Numerical Approach Towards the Correlation Between Ball Impact Test and Drop Reliability

A Numerical Approach Towards the Correlation Between Ball Impact Test and Drop Reliability Chang-Lin Yeh*, Yi-Shao Lai Stress-Reliability Lab, Advanced Semiconductor Engineering, Inc. 26 Chin 3 rd Rd., Nantze Export rocessing Zone, 811 Nantze, Kaohsiung, Taiwan *Email: chanlin_yeh@aseglobal.com Abstract The ball impact test is developed as a package-level measure for the board-level drop reliability of solder joints in the sense that it leads to fracturing of solder joints around the intermetallics, similar to that from a board-level drop test. In this paper, both board-level drop test and package-level ball impact test are examined numerically for solder joints of nine Sn-Ag-Cu solder compositions. Correlations between the drop reliability and characteristics of the impact force profile are sought. 1. Introduction The adoption of stiffer and more brittle lead-free solder alloys [1] along with the prevalence of mobile electronic devices brings the need of characterizing solder joint reliability under dynamic loads. The common way to characterize the reliability of solder joints is through boardlevel tests. For board-level test vehicles subjected to mechanical loads of reasonably high strain rates, it is frequently observed that fracturing occurs around the interface between the solder joint and its bonding pads, where intermetallic compounds (IMCs) develop [2-8]. Therefore, characterization of the strength of IMC is crucial to the assessment of reliability of solder joints under a dynamic loading condition. However, each solder joint in a board-level test vehicle connects to two bonding pads on the package side as well as the test board side. Quite often geometric configurations and surface finishes of the two pads are distinct [7]. It is therefore fairly difficult to specify a loading condition that allows fracturing to occur dominantly around a preferred pad, at which the IMC strength is to be examined. Considering the high cost and long duration a board-level test takes, direct testing on a package-level solder joint that involves only a single pad meets the demand more efficiently and economically. For a single package-level solder joint, the ball shear test that shears off the solder joint along the direction parallel to the pad is generally employed in the industry to evaluate the strength of the solder joint. This test is simple and convenient to implement. However, from both experiments and numerical analyses, it has been noted that a conventional low-strain- rate ball shear test with a crosshead speed slower than.1 mm/s seldom leads to fracturing of IMC [9]. The same situation also occurs when a number of solder joints on a board-level test vehicle are sheared off simultaneously [1]. Since a conventional ball shear test with a low shearing velocity is unable to reproduce the typical IMC fracturing failure mode encountered in a board-level drop test, it can be expected that there is hardly a chance for ball shear testing results to be correlated with the drop reliability. Apparently, if a test equipment capable of evaluating the IMC strength is to be developed based on the configuration of the ball shear test, the shearing velocity must be greatly enhanced [1,11-14]. Meanwhile, the test apparatus must be carefully designed to suppress structural resonance in order to obtain reliable force or acceleration measurements [15]. A high sampling rate data acquisition system is also a necessity. Efforts have been devoted to the empirical correlation between board-level drop reliability and characteristics of the impact force profile from the ball impact test (BIT) [14]. In this paper, both board-level drop test and package-level BIT are examined numerically. We consider different Sn-Ag-Cu solder joint compositions, namely, Sn-4Ag-Cu (), Sn-3Ag-Cu (), Sn-2.6Ag-.6Cu (), Sn- 1Ag-Cu (), and Sn-Ag-Cu solder alloys dopped with trace elements: Sn-Ag-Cu-Sb (),,,, and. Through numerical solutions, insights into the analytical correlation between the drop reliability and characteristics of the impact force profile are provided. 2. Board-level Drop Test We consider a 1 1.8 mm 3 thin-profile fine-pitch ball grid array (TFBGA) chip-scale package interconnected to a 132 77 1 mm 3 standard 8-layer JEDEC drop test board. The package contains a 5.5 5.5.25 mm 3 silicon die and a.26 mm thick substrate. The diameter and standoff of a solder joint are.35 mm and.21 mm, respectively. Openings of a solder joint on the package side and the test board side are.26 mm and.28 mm, respectively. The pitch between adjacent solder joints is mm. The mounting scheme of packages on the test board is shown in Fig. 1, following JESD22-B111 [16]. The figure also depicts the quarter symmetry modeling region for the finite element analysis. We consider the layout for which only the package at the center of the test board, U8, is implemented. 71 mm U6 U7 132 mm U11 U12 U13 U14 U15 U8 U9 U1 U1 U2 U3 U4 U5 15 mm Fixed end 77 mm Modeling region Fig. 1: Schematic of test board and modeling region 1-4244-665-X/6/$2 26 IEEE 161

Fig. 2 shows the finite element model of the board-level test vehicle around the package. The finite element model contains 5,127 linear hexahedral solid elements and 18,99 degrees of freedom. The structure of the solder joint is simplified in the way such that the two bonding pads are both neglected. The test vehicle is dropped with the package facing downward under JEDEC drop test condition B [16], for which a half-sine impact acceleration pulse with a peak acceleration of 15 G and a pulse duration of ms is prescribed. The transient analysis, which follows the support excitation scheme [17,18] and incorporates with the implicit time integration, is performed using ANSYS v. 1. solder alloys dopped with trace elements, namely,,,,, and. Fig. 3 shows stress-strain curves for these solder alloys, obtained from quasi-static uniaxial tensile tests on 1 6 3 mm 3 dog-bone specimens at a strain rate of approximately 2 1-4 s -1. We construct trilinear elastoplastic constitutive relationships for the solder alloys based on these curves. For all solder alloys, ν is.36 and ρ is 7.44 g/cm 3. Isotropic hardening is presumed. 4 35 3 Compound Die Fig. 2: Finite element mesh around the package Solder joint Test board Elastic properties of constituent components except for the solder alloy are presented in Table 1. material properties are assigned for the test board and the substrate, Table 2. In these tables, E is the Young s modulus, ν the oisson s ratio, ρ the mass density, and G the shear modulus. Note that z denotes the out-of-plane direction while x and y refer to in-plane directions. Mass-weighted damping and stiffness-weighted damping of the test vehicle are assumed 8 and 13, respectively. Table 1: Elastic properties of constituents Component E (Ga) ν ρ (g/cm 3 ) 1.91 Die 131.23 2.33 Compound 28.35 1.89 Test board 1.91 Table 2: Trnasversely properties for test board and substrate Test board E x, E y (Ga) 15.1 E z (Ga) 6.65 G xz, G yz (Ga) 6.82 G xy (Ga) 2.98 ν xz, ν yz.39 ν xy.11 E x, E y (Ga) 16.8 E z (Ga) 7.4 G xz, G yz (Ga) 7.59 G xy (Ga) 3.31 ν xz, ν yz.39 ν xy.11 In this study, we compare Sn-Ag-Cu solder alloys, namely,,,, and, and Sn-Ag-Cu Stress (Ma) 25 2 15 1 5 3.5 4. 4.5 5. Strain (%) Fig. 3: Stress-strain curves for solder alloys In reality, material properties of the solder alloy depend greatly on the process, test methodology, and specimen size. In this regard, the actual mechanical response of the solder joint is quite difficult to obtain. The strain rate effect is ignored in this study since it is particularly difficult to identify without proper experimental measurements. Moreover, as of now, there are no suitable rate-dependent constitutive relationships for lead-free solder alloys that suit JEDEC drop test conditions, for which the strain rate is up to around 1 2 s -1 [5]. We denote normal stress, shear stress, and equivalent plastic strain as σ n, σ s, and ε p, respectively. Here σ n stands for the normal component whereas σ s the squared-root sum of the two shear components of the surface traction. Fig. 4 shows the most critical solder joint and the locations where maximum σ n, σ s, and ε p occur during the course of the drop impact. y Maximum σ n Maximum σ s Maximum ε p z ackage side Test board side x Fig. 4: Locations of maximum σ n, σ s, and ε p x A B D C 162

Table 3 summarizes maximum σ n, σ s, and ε p experienced on the package side of the most critical solder joint during the course of the drop impact. Table 3: Maximum σ n, σ s, and ε p Solder alloy σ n (Ma) σ s (Ma) ε p (%) 17.6 44.16 6.831 1 44.44 7.577 93.45 33.67 8.265 76.34 28.53 175 1.1 37.51 7.53 92.25 4.9 8.86 1 45.27 7.57 96.44 43.15 8.36 15.9 39.62 6.675 experiences force concentration around the contact region with the pin, incurring large deformations. To avoid hourglassing, a numerically instable feature particularly for linear hexahedral solid elements subjected to a concentrated force, linear tetrahedral elements are applied on the regions depicted in Fig. 7. We neglect IMC in the numerical model since it is too thin to be implemented [24]. The transient analysis is performed using ANSYS/LS-DYNA v. 97. 24 V i = 1.4 m/s in 3 Solder 24 Fig. 5 shows stress loci of σ n -σ s for different solder joint compositions at oint A, where maximum σ n occurs on the package side of the critical solder joint, from the onset of the drop impact to when the peak σ n occurs. Apparently, during the course of the drop impact, σ n is about 5.25 times greater than σ s at oint A. 16 22 Soldermask ad 24 4 8 Soldermask 18 15 12 5.25 Fig. 6: hysical model for BIT (unit: µm, not to the scale) σ s (Ma) 1 8 4-4 -2 2 4 6 8 σ n (Ma) Fig. 5: Stress loci of σ n -σ s at oint A during drop impact 3. Ball Impact Test The numerical methodology that deals with transient fracturing of a package-level solder joint subjected to a displacement-controlled impact load has been developed by Yeh and coworkers [19-25]. In this study, we follow the same methodology to examine transient impact force responses of the solder joints with different solder compositions. The physical model for BIT is shown in Fig. 6. A rigid pin moves horizontally from left to right and strikes on the package-level solder joint with a constant impact velocity, V i. In this study, we assume V i = 1.4 m/s. It has been realized that when the IMC strength is not great enough, different V i do not bring significantly different impact force responses [24]. Fig. 7 shows the three-dimensional symmetric finite element model for the test vehicle. For components other than the solder joint, linear hexahedral solid elements are applied. Since the solder joint is spherical, at the onset of impact, it Fig. 7: Symmetric finite element model Fracturing of the test vehicle can be categorized into two different types: fracturing within the solder alloy and interfacial fracturing between solder alloy and pad, at which IMC develops. Adequate fracturing mechanisms and corresponding failure criteria are therefore required to characterize the path of fracture propagation subjected to an impact load. Considering that fracturing within the solder alloy is a failure mode secondary to IMC fracturing during drop impacts [5-8], in this study, we focus on interfacial IMC fracturing of the package-level solder joint only. Interfacial IMC fracturing is modeled using the tiebreak nodes-to-surface contact [24], which links adjacent meshes and confines the movements of nodes until the bond breaks. The bond failure is characterized by 163

f S n n C f + S n C s where the subscripts n and s denote normal and shear, respectively, and f and S the weld force and the ultimate force when the bond breaks, respectively. In this study, an elliptical failure envelope, C n = C s = 2, is adopted. Moreover, the shear strength of IMC is assumed to be two times greater than the normal strength of IMC. That is, S s = 2 S n = 2 σ A e, in which A e is the equivalent area of the contact element while σ the tensile IMC strength in terms of the stress. Note that this merely represents an assumption and requires further experimental work to justify. Characteristics of the impact force profile can be defined according to Fig. 8. Since the post-failure structural behavior of the solder joint is extremely complicated and hardly reproducible, we consider only the ascending part of the primary peak of the impact force profile, which stands for the structural behavior of the solder joint from the initiation of the impact load till fracturing starts. s s 1 (1) impact process, we have S r Vi Kr, where K r stands for the equivalent stiffness of the solder joint. Figs. 9, 1, and 11 show, E r, and d r with respect to σ, respectively, for different solder alloys. σ (Ma) 3 25 2 15 1 5 3.5 4. (N) Fig. 9: with respect to σ 3 1 25 Force.1 S r A r τ r Time Fig. 8: Typical impact force profile σ (Ma) 2 15 1 5 15 3 45 6 75 9 E r (µj) Characteristics of the typical impact force profile depicted in Fig. 8 and those derived from these characteristics are described in the following: 1. : The maximum impact force, or the impact resistance, which relates to the IMC strength. 2. τ r : The duration of the ascending part of the impact force profile, which stands for the ductility, d r, of the solder joint. If V i varies insignificantly during the entire impact process, we have d r V i τ r, which also stands for the stroke from the onset of the impact till fracturing starts. 3. A r : The area below the ascending part of the impact force profile, which represents the toughness of the solder joint. This quantity is proportional to the impact energy exerted during the ascending part, E r. If V i varies insignificantly during the entire impact process, we have E i Vi Ar. 4. S r : The slope of the ascending part of the impact force profile. If V i varies insignificantly during the entire σ (Ma) 3 25 2 15 1 5 Fig. 1: E r with with respect to σ 1 2 3 4 5 d r (µm) Fig. 11: d r with respect to σ 164

Fig. 12 shows stress loci of f n -f s at oint A for different solder joint compositions during BIT. It is clear that the slope is approximately 1.23 and is nearly independent of solder compositions. the figures that, E r, and d r are not particularly good BIT indices to correlate with the drop reliability index because the correlations are not universal; they vary according to different solder compositions. 25 f s (mn) 2 15 1 5 5 1 15 2 25 f n (mn) 1.23 1 1 2 3 4 (N) Fig. 12: Stress loci of f n -f s at oint A during BIT Comparing between stress loci at oint A induced by the board-level drop test, Fig. 5, and those induced by BIT, Fig. 12, we note that σ n plays a more significant role in the failure mechanism of a board-level drop test rather than that of BIT. Also noted is that these slopes are different from those obtained in our previous numerical studies [24,26] because of different constitutive relationships for the solder alloys. 4. Reliability Indices Interfacial IMC fracturing is the primary failure mode of solder joints under drop impacts, in particular for lead-free solder joints [5-8]. From the previous analysis, σ n is also found to be several times greater than σ s. We therefore assume that the mean value of the drop count to failure, N f, is proportional to σ while inversely proportional to the maximum σ n in a power-law formulation such that Fig. 13: versus 2 4 6 8 E r (µj) b σ N f = a (2) σ n where a and b are universal constants independent of structures, materials, and assembly processes. We define σ = (3) σ n Fig. 14: versus E r as the drop reliability index. A larger indicates a better drop reliability. Note that, ideally, σ n is obtained from the transient analysis for the board-level drop test while σ is identified by correlating transient analysis for BIT with the measured impact force profile. In this study, however, due to the lack of BIT measurements, σ is a prescribed magnitude. Following this concept, we plot with respect to, E r, and d r in Figs. 13, 14, and 15, respectively. It is apparent from 1 2 3 4 5 d r (µm) Fig. 15: versus d r 165

From Figs. 13 through 15, we note that curves for solder joints of different compositions are close when E r is small. This indicates that, compared to or d r, under the circumstance that is small, E r or a physical term related to the impact energy serves as a good indicator of drop reliability of board-level solder joints regardless of their compositions. This particular feature has been reported by Wong et al. [1] and Yeh et al. [14] from experimental observations. However, when σ of the solder joint increases, plasticity develops around the location where fracturing initiates [25], and hence the curves vary significantly according to different solder compositions. Consequently, the correlations between and these BIT characteristics become non-universal. To obtain universal correlations between and these BIT characteristics, here we propose to multiply, E r, and d r by constant multipliers, f a, f b, and f c, respectively. Magnitudes of these multipliers are listed in Table 4 for different solder alloys. Note that these magnitudes are empirically selected without a theoretical background. 1 2 3 4 5 6 7 8 9 f b E r (µj) Fig. 17: versus f b E r Table 4: Multipliers for different solder alloys Solder alloy f a f b f c 1.1 1.1.9 5.7 1.1.6.6.9.65.8 1.1.85 1.1 1.15 1.15 1.1.95.9.7.85 Correlations between and f a, f b E r, and f c d r are plotted in Figs. 16, 17, and 18, respectively. With the empirical multipliers, the modified correlations appear to be universal, i.e., independent of solder compositions. However, physical meanings of these multipliers certainly require further investigations. 3.5 4. f a (N) Fig. 16: versus f a 1 2 3 4 5 f c D r (µm) Fig. 18: versus f c d r 5. Conclusion Board-level drop test and package-level BIT are examined numerically in this paper. Different Sn-Ag-Cu solder joint compositions, namely,,,, and, and Sn-Ag-Cu solder alloys dopped with trace elements, namely,,,,, and, are considered. Through numerical solutions, insights into the analytical correlation between the drop reliability and characteristics of the impact force profile are provided. We note that and d r are not particularly good BIT indices to correlate with board-level drop reliability because their correlations are not universal, varying according to different compositions of the solder joints. Nevertheless, E r can be a reasonably good indicator as long as is small. Although the correlations become universal by introducing constant multipliers to these indices, physical meanings of these empirically chosen multipliers certainly require further investigations. Besides, numerical solutions presented in this paper follow rate-independent constitutive relationships for 166

the solder alloys. For these dynamic problems, rate-dependent constitutive relationships are in serious need. Acknowledgment Solder samples examined in this study were provided by Accurus Scientific Co., Ltd. (Tainan, Taiwan), a joint development partener with ASE Group on solder alloys and soldering technologies. References 1. Wong, E. H. et al, Drop Impact: Fundamentals and Impact Characterisation of Solder Joints, roc. 55 th Electr. Comp. Technol. Conf., Lake Buena Vista, FL, 25, pp. 122-129. 2. Moon, H. J. et al, Brittle Fracture of b-free Solder Joint in Ni/Au Finished FBGA MC Mounted on OS Board Subjected to Bending Impact Load, roc. 37 th Int. Symp. Microelectr., Long Beach, CA, 24. 3. Lai, Y.-S. et al, Board-level Drop erformance of Leadfree chip-scale ackages with Different Soldermask Openings and Solder Compositions, roc. 6 th Int. Conf. Electr. Mater. ack., enang, Malaysia, 24, pp. 56-6. 4. Reiff, D. and Bradley, E., A Novel Mechanical Shock Test Method to Evaluate Lead-free BGA Solder Joint Reliability, roc. 55 th Electr. Comp. Technol. Conf., Lake Buena Vista, FL, 25, pp. 1519-1525. 5. Lai, Y.-S. et al, Impact of Various JEDEC Drop Test Conditions on Board-level Reliability of Chip-scale ackages, roc. 38 th Int. Symp. Microelectr., hiladelphia, A, 25, pp. 199-25. 6. Birzer, C. et al, Drop Test Reliability Improvement of Lead-free Fine itch BGA Using Different Solder Ball Composition, roc. 7 th Electr. ack. Technol. Conf., Singapore, 25, pp. 255-261. 7. Lai, Y.-S. et al, Experimental Studies of Board-level Reliability of Chip-scale ackages Subjected to JEDEC Drop Test Condition, Microelectr. Reliab. Vol. 46, No. 2-4 (26), pp. 645-65. 8. Chong, D. Y. R. et al, Drop Impact Reliability Testing for Lead-free and Lead-based Soldered IC ackages, Microelectr. Reliab., Vol. 46, No. 7 (26), pp. 116-1171. 9. Huang, X. et al, Characterization and Analysis on the Solder Ball Shear Testing Conditions, roc. 51 st Electr. Comp. Technol. Conf., Orlando, FL, 21, pp. 165-171. 1. Canumalla, S. et al, ackage to Board Inter-connection Shear Strength (BISS): Effect of Surface Finish, WB Build-up Layer and Chip Scale ackage Structure, IEEE Trans. Comp. ack. Technol. Vol. 27, No. 1 (24), pp. 182-19. 11. Date, M. et al, Ductile-to-brittle Transition in Sn-Zn Solder Joints Measured by Impact Test, Scripta Mater. Vol. 51 (24), pp. 641-645. 12. Ou, S. et al, Micro-impact Test on Lead-free BGA Balls on Au/Electrolytic Ni/Cu Bond ad, roc. 55 th Electr. Comp. Technol. Conf., Lake Buena Vista, FL, 25, pp. 467-471. 13. Newman, K., BGA Brittle Fracture Alternative Solder Joint Integrity Test Methods, roc. 55 th Electr. Comp. Technol. Conf., Lake Buena Vista, FL, 25, pp. 1194-121. 14. Yeh, C.-L. et al, Empirical Correlation Between ackage-level Ball Impact Test and Board-level Drop Reliability, Microelectr. Reliab., in press. 15. Yeh, C.-L. and Lai, Y.-S., Design Guideline for Ball Impact Test Apparatus, J. Electr. ack., ASME, in press. 16. JEDEC Solid State Technology Association, JESD22- B111: Board Level Drop Test Method of Component for Handheld Electronics roducts, 23. 17. Yeh, C.-L. and Lai, Y.-S., Support Excitation Scheme for Transient Analysis of JEDEC Board-level Drop Test, Microelectr. Reliab. Vol. 46, No. 2-4 (26), pp. 626-636. 18. Yeh, C.-L. et al, Evaluation of Board-level Reliability of Electronic ackages Under Consecutive Drops, Microelectr. Reliab., Vol. 46, No. 7 (26), pp. 1172-1182. 19. Yeh, C.-L. et al, Transient Deformation and Fracturing of Solder Joints Subjected to Impact Loads, roc IMAS Flip Chip 24, Austin, TX, 24. 2. Yeh, C.-L. and Lai, Y.-S., Transient Analysis of Fracturing Modes of Solder Joints Subjected to Impact Loads, roc. 24 Taiwan ANSYS Conf., Nantou, Taiwan, 24, pp. 25-3. 21. Yeh, C.-L. and Lai, Y.-S., Transient Simulation of Solder Joint Fracturing Under Impact Test, roc 6 th Electr. ack. Technol. Conf., Singapore, 24, pp. 689-694. 22. Yeh, C.-L. and Lai, Y.-S., Transient Analysis of Impact Fracturing of Solder Joints, roc. EuroSimE 25, Berlin, Germany, 25, pp. 53-59. 23. Yeh, C.-L. et al, Numerical Investigations of Displacement-controlled Impact Loads on Solder Joints, roc. IMAS Taiwan 25 Int. Tech. Symp., Taipei, Taiwan, 25, pp. 44-49. 24. Yeh, C.-L. and Lai, Y.-S., Transient Fracturing of Solder Joints Subjected to Displacement-controlled Impact Loads, Microelectr. Reliab., Vol. 46, No. 5-6 (26), pp. 885-895. 25. Yeh, C.-L. and Lai, Y.-S., Effects of Solder Alloy Constitutive Relationships on Impact Force Responses of ackage-level Solder Joints Under Ball Impact Test, J. Electr. Mater., in press. 26. Yeh, C.-L. et al, rediction of Board-level Drop Reliability of Chip-scale ackages with Experimental Verifications, roc. 38 th Int. Symp. Microelectr., hiladelphia, A, 25, pp. 586-593. 167